The Church

The Assembly of the Eighth Sacrament is a special agency made up of a group of special clerics charged with the research, recovery, and managing of holy relics scattered across the globe. The members follow the "Eighth Sacrament" outside of the Sacraments of the Catholic Church, the seven graces that God bestowed: Baptism, Holy Eucharist, Matrimony, Holy Orders, Confirmation, Penance, Anointing. It is a "power separated from the faith", meaning the members trained to retrieve the hidden relics do not fear being involved in heretical power such as magecraft to accomplish their goals.

The Executors are the heretic inquisitors of the Holy Church established by the 120th Cardinal. They have the task of demon killing and the destruction of other heretical beings.

It is known as the bloodiest department of the Church, called the Shura's Den for its responsibility of punishing heresies. It takes a certain amount of willpower to be part of it, and being able to achieve the title of "Executor" signifies that one is a first-rate murderer that has passed brutal and pious training to become mankind's weapon.
One of the ironclad rules of the Holy Church is that Executors operating in the field are granted complete independent authority to resolve the incident until their task is complete, and not even someone at the top of the organization’s hierarchy have the authority to interfere with them while they are under this protection. Despite this high degree of autonomy, the Executors are of low rank in the Church’s hierarchy. They are disposable soldiers who exist to fight and die on the battlefield.

The Executors also follow the "Eighth Sacrament" granting the permit to stray away from the rules of their religion as long as one thing, the name of the Almighty, is protected. They are followers that do not teach the words of the Lord, but act as His representative, His Executors, despite being mere mortals.

The Burial Agency is a group of special Inquisitors gathered by the Holy Church. A secret division of the Holy Church, an organization of Europe's prominent religion whose name means "universal".

It comprises seven Executors. A walking Armory; a security force consisting of a mere handful of people. They are in charge of exterminating the "inhuman things" that never show themselves, which the Church condemned as heresies — Vampires.

When it comes to the Executors of the Burial Agency, they will stop at nothing if it's to apprehend a Dead Apostle, even having a whole town disappear from the map. They have the authority where whatever they do is allowed if their opponent is a vampire, and that includes the city targeted by the Dead Apostle: whether humans still live there or not, if it's an already defiled land, they will burn it down all the same. For the Burial Agency, being a non-human Prime Species is on its own "evil".
"Prime Species" refers simply to a world's dominant species, and does not necessarily imply the intelligence to form civilization.

There is an eighth reserve member, but they are not granted the same privilege. The privilege of independent action permitted by the Archbishop are the 7 members only, therefore it was decided that adding more than that would be dangerous.

Wraith, also referred to as Ghosts or Human Spirits, are souls of dead people that remain attached to this world due to past grudges, regrets and other sorts of unfinished business that they had during life. However, as they are no longer something that belongs to this world, their existence is something that degrades with time and they are bound to disappear eventually.

Normally, direct physical interference on the part of these Ghosts are low. As Spiritual Bodies they usually have to act through some sort of medium.

As Human Spirits they are able to consume the souls and minds of people and convert them into energy. The basic abilities they had from the time when they where alive still remain but they don't change from such nourishment, as they only become tougher as their Magical Energy capacity increases.

Demons are existences that, while being of the Laws of Nature, disturb its flow. The distortion that these cause to their surroundings is rather high, requiring them to be put down.

The Sixth Imaginary Factor also known as Daemons, is a force that reacts to the desires of humans and births Daemons out of their wishes. It needs a form, invented by humans, in order to materialize itself as a passive existence. This passive existence is an individual Daemon and not a True Daemon.
But regardless of the result, as a rule, Daemons are gentle. They are the Imaginary Factor that understands one's pain and attempts to remove it. Depending on perspective, one can say that they are allies of humanity. They act to realize the wishes they come to be invested within by distorted means.

In general, a Daemon usually takes possession of the human that birthed it. But in the event that the mind of the host cannot withstand the strain, it is common for the self-destruction of the host to occur, dispersing the essence of the Daemon into the vicinity. Upon possession by a daemon, irregularities manifest in the the victim's body, eventually rendering them as grotesque monsters by the metamorphosis of the flesh, once this process is complete they become a mature Daemon.

Daemons need something called a Unit Designation to be free, while True Daemons don't, what does that mean? what are true daemons exactly? idk, this is not something very well explored in the nasuverse all we know is True Daemons strong a fuckload.

Anyone who studied magecraft knows this, whether from the Mage's Association, the church, or a standalone guy.
Info known by higher positions or specific fields in The Mage's Association.
Info known by people of the church.
Info known by Specific divisions of the church of the Church.